Sub-flux quantum generator

ABSTRACT

A sub-flux quantum generator includes an N-turn ring having a plurality of connected turns about a common aperture. The width of each respective turn in the N-turn ring exceeds the London penetration depth of a superconducting material used to make the respective turn. The generator includes a switching device configured to introduce a reversible localized break in the superconductivity of at least one turn in the N-turn ring. The generator includes a magnetism device configured to generate a magnetic field within the aperture of the N-turn ring. A method for biasing a superconducting structure that encompasses all or a portion of an N-turn ring. While a supercurrent is flowing through the N-turn ring, a quantized magnetic flux is introduced into the aperture of the N-turn ring using a reversible localized break in a turn in the ring. The quantized magnetic flux is trapped in the ring by removal of the localized break. The trapped flux biases the superconducting structure.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims benefit, under 35 U.S.C. § 119(e), of U.S.Provisional Patent Application No. 60/383,579 filed on May 24, 2002which is incorporated herein, by reference, in its entirety.

FIELD OF THE INVENTION

This invention relates to superconducting circuitry. More specifically,this invention relates to devices that generate fractions of a fluxquantum.

BACKGROUND

Quantum computing is accomplished using the effects of qubits thatexhibit quantum mechanical behavior. A qubit is a physical system thatis restricted to two or more energy states. A qubit is a quantum bit,the counterpart in quantum computing to the binary digit or bit ofclassical computing. Just as a bit is the basic unit of information in aclassical computer, a qubit is the basic unit of information in aquantum computer. A qubit is conventionally a system having two or morediscrete energy states. The energy states of a qubit are generallyreferred to as the basis states of the qubit. The basis states of aqubit are termed the |0> and |1> basis states. Typically, in quantumcomputing applications, a qubit is placed (e.g., biased) to a statewhere two of the discrete energy states of the qubit are degenerate.Energy states are degenerate when they possess the same energy.

A qubit can be in any superposition of two basis states, making itfundamentally different from a bit in an ordinary digital computer. Asuperposition of basis states arises in a qubit when there is a non-zeroprobability that the system occupies more than one of the basis statesat a given time. Qualitatively, a superposition of basis states meansthat the qubit can be in both basis states |0> and |1> at the same time.Mathematically, a superposition of basis states means that the overallstate of the qubit, which is denoted |Ψ>, has the form|Ψ>=a|0>+b|1>where a and b are coefficients respectively corresponding to probabilityamplitudes |a|² and |b|². The coefficients a and b each have real andimaginary components, which allows the phase of qubit to be modeled. Thequantum nature of a qubit is largely derived from its ability to existin a superposition of basis states, and for the state of the qubit tohave a phase.

If certain conditions are satisfied, N qubits can define a state that isa combination of 2^(N) classical states. This state undergoes evolution,governed by the interactions that the qubits have among themselves andwith external influences, providing quantum mechanical operations thathave no analogy with classical computing. The evolution of the states ofN qubits defines a calculation or, in effect, 2^(N) simultaneousclassical calculations. Reading out the states of the qubits afterevolution completely determines the results of the calculations.

It is held by some in the art that certain quantum computing algorithms,such as the Shor algorithm, require that the number of qubits in thequantum computer must be at least 10⁴. See Mooij et al., 1999, Science285, p. 1036, which is hereby incorporated by reference in its entirety.Qubits have been implemented in cavity quantum dynamic systems, iontraps, and nuclear spins of large numbers of identical molecules.However, such systems are not particularly well suited for therealization of the desired high number of interacting qubits needed in aquantum computer. A survey of the current physical systems from whichqubits can be formed is Braunstein and Lo (eds.), Scalable QuantumComputers, Wiley-VCH Verlag GmbH, Berlin (2001), which is herebyincorporated by reference in its entirety. Of the various physicalsystems surveyed, the systems that appear to be most suited for scaling(e.g., combined in such a manner that they interact with each other) arethose physical systems that include superconducting structures such assuperconducting qubits.

A proposal to build a scalable quantum computer from superconductingqubits was published in 1997. See Bocko et al., 1997, IEEE Trans. Appl.Supercon. 7, p. 3638, and Makhlin et al., 2001, Rev. of Mod. Phys., 73,p. 357, which are hereby incorporated by reference in their entireties.Since then, many designs have been introduced. One such design is thepersistent current qubit. See Mooij et al., 1999, Science 285, 1036; andOrlando et al., 1999, Phys. Rev. B 60, 15398, which are herebyincorporated by reference in their entireties.

A description of the persistent current qubit, as described in Mooij etal., is illustrated by circuit 700 in FIG. 7. Circuit 700 consists of aloop with three small-capacitance Josephson junctions (702-1, 702-2, and702-3) in series. In operation, circuit 700 encloses a magnetic fluxƒM_(o). Here, M_(o) is the superconducting flux quantum h/2e (i.e.,fluxon, flux quantum) where h is Plank's constant and e is elementarycharge. See Tinkham, Introduction to Superconductivity, McGraw-Hill,Inc., New York, 1996, which is hereby incorporated by reference in itsentirety, for a theoretical description of the fluxon. In operation, themagnetic ƒM_(o) enclosed by circuit 700 is created by applying anexternal magnetic flux with magnitude ƒM_(o) to circuit 700. Thisexternal magnetic flux is referred to as an applied magnetic flux,applied magnetic frustration, or simply frustration flux. Two of thejunctions 702 in circuit 700 have equal Josephson coupling energiesE_(J). The Josephson coupling energy of the third junction 702 is lessthan the coupling energy E_(J) of the first two junctions 702.Typically, the Josephson energy of the third junction 702 is αE_(j),with 0.5<α<1.

An important feature of the Josephson energy in circuit 700 is that itis a function of two phases. For a range of frustration fluxes ƒM_(o),where ƒ represents some range of numbers, these two phases permit twostable configurations that correspond to dc currents flowing in oppositedirections. In fact, for ƒ=0.5 (i.e., 0.5×M_(o), one half a fluxon), theenergies of the two stable configurations (states) are the same (aredegenerate). Thus, when an external magnetic force having the magnitudeƒM_(o) (where ƒ=0.5) is applied against circuit 700, the circuit acts asa persistent current qubit with two degenerate states. One of thedegenerate states, represented by a clockwise dc current 720 circulatingin circuit 700, may be arbitrarily assigned the basis state |0>. Thenthe other degenerate state, represented by a counterclockwise dc current722 circulating in circuit 700, is assigned the basis state |1>. Anotherproperty of circuit 700 is that the barrier for quantum tunnelingbetween the two degenerate states depends strongly on the value α Largervalues α (i.e., higher Josephson energy in the third junction 702)result in higher tunneling barriers.

One advantage of superconducting qubits is that they are scalable. Adisadvantage of persistent current qubit 700 is that it is difficult toprovide a stable source for the applied magnetic flux ƒM_(o) that isnecessary to produce the two degenerate states. Fluctuations in thefrustration flux can decohere the states of the qubit making computationdifficult or unreliable. Decoherence is the loss of the phases ofquantum superpositions in a qubit as a result of interactions with theenvironment. Thus, decoherence results in the loss of the superpositionof basis states in a qubit. See, for example, Zurek, 1991, Phys. Today44, p. 36; Leggett et al., 1987, Rev. Mod. Phys. 59, p. 1; Weiss, 1999,Quantitative Dissipative Systems, 2^(nd) ed., World Scientific,Singapore; Hu et al; arXiv:cond-mat/0108339, which are hereinincorporated by reference in their entireties. Inductance from normalelectronics is not suitable for producing degenerate states in apersistent current qubit. Any disruption in the current through suchelectronics will disrupt the degenerate states. Vibrations of the systemcan cause a change in the level of frustration (level of bias). Even thebriefest interruption in the degeneracy of the states will destroy thequantum computation performed on the qubit.

One approach to trap flux is through flux quantization in a ring ofsuperconducting material that has a cross section that is larger thanthe London penetration depth λ_(L). In this approach, an external fluxof about one flux quantum is applied to ring while cooling the ring downthrough the superconducting phase transition. Once below thesuperconducting phase transition temperature, the center of the ring(the aperture of the ring) will have a magnetic flux of one flux quantumbecause it will be trapped by the surrounding superconducting material.Then, the external field is removed. When the external magnetic field isremoved in a nonsuperconducting ring, the magnetic flux in the center ofthe ring pierces the ring and is annihilated. However, this is notpossible in a superconducting ring because the magnetic flux trapped inthe center of the ring cannot penetrate the superconducting ring. Thus,in this way, a ring is capable of trapping magnetic field in multiplesof the magnetic flux quantum (i.e., 1×h/2e, 2×h/2e, 3×h/2e, and soforth). The flux is quantized because the wavefunction of thesupercurrent is naturally single valued. This means the integral of thephase around the ring of superconducting material should be a multipleof 2π.

One possibility for providing an applied magnetic flux to a persistentcurrent qubit is a superconducting ring recently proposed by Majer etal. See Majer et al., 2002, Applied Physics Letters 80, p. 3638 which ishereby incorporated by reference in its entirety. Majer et al. proposeda mesoscopic (e.g., having a diameter of 3 μm) superconducting ring 800(FIG. 8) that has no junctions. A superconducting material is a materialthat has zero electrical resistance below critical levels of current,magnetic field and temperature. The Majer et al. ring has a crosssection 802 that is narrower than the London penetration depth λ_(L) ofthe ring. The London penetration depth λ_(L) describes the exponentiallydecaying magnetic field in layers just below the surface of asuperconductor. In general, magnetic fields are excluded withinsuperconducting materials. The exclusion of magnetic fields deep in asuperconducting material is known as the Meissner effect. However, inshallow layers just below the surface of superconducting materials, theextent to which magnetic fields are excluded is exponentially dependenton the distance between the layer and the surface of the superconductor.The London penetration depth λ_(L) of a superconducting material is thedistance from the material surface to a point in the material wheremagnetic flux is e⁻¹ times less than at the material surface. Here, e isthe base of the natural logarithm. London penetration depth is materialdependent but typically on the order of 500 Å for some superconductingmaterials.

As mentioned above, the ring proposed by Majer et al. has a crosssection 802 that is narrower than the London penetration depth λ of thering. However, the ring 800 can be used to trap magnetic flux throughthe phenomena of fluxoid quantization, which is a distinctly differentphenomena than the phenomena of flux quantization described above. Thedifference between flouxoid quantization and flux quantization is that,although the resultant magnetic field is the same, the origins of themagnetic field differ. In flux quantization of a thick ring, themagnetic field in the ring is comprised of a trapped magnetic field. Influxiod quantization of a ring that is narrower than the Londonpenetration depth of the ring, the magnetic field in the ring is inducedby circulating current that remains in the ring. See M. Tinkham, 1996,Introduction to Superconductivity, McGraw Hill, which is herebyincorporated by reference in its entirety. In one approach, an externalflux quantum is applied to ring 800 while cooling the ring down throughthe superconducting phase transition. The center of ring 800 will have amagnetic flux quantum because of the presence of the external magneticflux. Then, once ring 800 is superconducting, the external field isremoved. When the external magnetic field is removed in anonsuperconducting ring, the magnetic flux in the center of the ringpierces the ring and is annihilated. However, this is not possible inthe ring proposed by Majer et al. because the magnetic flux is inducedin the center of the ring by superconducting current in the ring. Asuperconducting ring is capable of trapping magnetic field in multiplesof the magnetic flux quantum (i.e., 1×h/2e, 2×h/2e, 3×h/2e, and soforth). The magnetic field is comprised of the trapped flux and the fluxgenerated by the circulating current. The Majer et al. ring provides nomechanism for releasing trapped magnetic flux. The trapped magnetic fluxcan be used as a source for applying a stable magnetic field to apersistent current qubit. The trapped magnetic flux in the Majer et al.ring is advantageous because it is not sensitive to fluctuations inapplied current. In fact, no applied current is required to maintain thetrapped magnetic flux in the Majer et al. ring 800 once it has beentrapped in the aperture of the ring.

While ring 800 represents a significant achievement in the art, it doesnot provide a satisfactory device for applying an external biasing(frustrating) magnetic field to a persistent current qubit for tworeasons. First, ring 800 does not provide a mechanism for trapping orreleasing trapped magnetic flux. The only way to trap or release thetrapped magnetic flux in ring 800 is to destroy the superconductingproperties of the ring. This can be accomplished, for example, byraising the temperature of the ring through the critical temperatureT_(C) of the superconducting material used to manufacture the ring.Second, ring 800 is not capable of trapping sub-fluxon quantities ofmagnetic flux. That is, ring 800 is not capable of trapping a magneticflux having a magnitude that is a fraction of h/2e. Yet, many persistentcurrent qubits, such as circuit 700, require an external magnetic forcehaving a magnitude that is a fraction of a fluxon in order to achievetwo degenerate states.

Given the above background, what is needed in the art is a mechanism fordelivering a stable and switchable flux source with sub-fluxonprecision.

Discussion or citation of a reference herein shall not be construed asan admission that such reference is prior art to the present invention.

SUMMARY OF THE INVENTION

The present invention provides a switchable stable sub-flux quantumgenerator. In one embodiment of the invention, an N-turn ring is used totrap fluxon or sub-fluxon amounts of magnetic flux. Furthermore, eachturn of the N-turn ring includes a switch. By regulating the switches inthe N-turn ring, the amount of magnetic flux in the N-turn ring can beused to control the amount of magnetic flux trapped within the ring withsub-fluxon precision. The switchable N-turn ring provides a reliableexternal magnetic flux that can be used to bias a persistent currentqubit, such as circuit 700, so that the two stable states of the qubitare degenerate.

One embodiment of the present invention provides a sub-flux quantumgenerator. The sub-flux quantum generator comprises an N-turn ring thatincludes N connected turns, where N is an integer greater than or equalto two. Further, each turn in the N-turn ring has a width that exceedsthe London penetration depth λ_(L) of the superconducting material usedto make each turn in the N-turn ring. The sub-flux quantum generatorfurther comprises a switching device that introduces a reversiblelocalized break in the superconductivity of at least one turn in theN-turn ring. The sub-flux quantum generator also includes a magnetismdevice that generates a magnetic field within the N-turn ring.

In some embodiments, the sub-flux quantum generator includes a set ofleads that is attached to the N-turn ring. The magnetism device is inelectrical communication with the set of leads in order to drive acurrent through the N-turn ring. In some embodiments of the presentinvention, the superconducting material used to make a turn in theN-turn ring is a type I superconductor such as niobium or aluminum. Insome embodiments of the present invention, the superconducting materialused to make a turn in the N-turn ring is a type II superconductor.

In some embodiments, the switching device in sub-flux quantum generatoris a cryotron that encompasses a portion of one or more of the turns inthe N-turn ring. In some embodiments, the switching device in thesub-flux quantum generator is a Josephson junction that is capable oftoggling between a superconducting zero voltage state and anonsuperconducting voltage state. In some embodiments, this Josephsonjunction includes a set of critical current leads that are used to drivea critical current through the Josephson junction to toggle theJosephson junction between the superconducting zero voltage state andthe nonsuperconducting voltage state.

Another aspect of the present invention provides a superconductingdevice comprising an outer structure and an inner structure. The outerstructure comprises a superconducting ring that encompasses at least aportion of the inner structure. This superconducting ring includes atleast one Josephson junction. The inner structure comprises an N-turnring that includes N connected turns. Turns are connected when they makecontact with each other. In some embodiments, the turns are twined.However, there is no requirement that the turns in an N-turn ring twine(twist) about each other in an N-turn ring. In some embodiments, allthat is required is that each turn in an N-turn ring make contact withat least one other turn in the N-turn ring. As used herein, the value Nfor the N-turn ring means an integer greater than or equal to two.Further, each turn in the N-turn ring has a width that exceeds theLondon penetration depth λ_(L) of a superconducting material used tomake each turn in the N-turn ring. In some embodiments of the presentinvention, the outer structure is a qubit, such as a phase qubit, ormore specifically, a persistent current qubit. In some embodiments, theinner structure further comprises a switching device that is capable ofintroducing a reversible localized break in the superconductivity of atleast one turn in the N-turn ring.

Another aspect of the present invention provides a method for trapping aquantized magnetic flux in an N-turn ring. Here, N is an integer greaterthan or equal to two. In the method, a supercurrent is allowed to flowthrough the N-turn ring. Next, a quantized magnetic flux Φ_(X) isinduced in an aperture of the N-turn ring by introducing a localizedbreak in a turn in the N-turn ring. This localized break interrupts thesupercurrent in a portion of the turn. Later, the supercurrent isrestored to the effected portion of the turn by removing the localizedbreak, thereby trapping the quantized magnetic flux in the N-turn ring.In some embodiments, the localized break in the turn is introduced bypassing a bias current through a Josephson junction present in theportion of the turn. The bias current causes the Josephson junction totoggle from a superconducting zero voltage state to a nonsuperconductingvoltage state.

Still another aspect of the present invention provides a method forfrustrating (biasing) a superconducting structure that encompasses aportion of an N-turn ring (where N is an integer equal to two orgreater). In the method, supercurrent is allowed to flow through theN-turn ring. Next, a quantized magnetic flux Φ_(X) is induced in anaperture of the N-turn ring by introducing a localized break in a turnin the N-turn ring. The localized break interrupts the supercurrent inthe portion of the turn. Then the quantized magnetic flux is trapped inthe N-turn ring by removing the localized break and restoring thesupercurrent to the effected portion of the turn, thereby frustratingthe superconducting structure that encompasses the portion of the N-turnring.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the relationship between generalized components ofone embodiment of the present invention, including an N-turn ring, aswitching device, and a magnetism device.

FIGS. 2A-2D illustrate a method for manufacturing an N-turn ring inaccordance with an embodiment of the present invention.

FIGS. 3A-3G illustrate various devices (cyclotron, FIGS. 3A-3C;Josephson junction, FIGS. 3D-3F; and laser, FIG. 3G) that can locallybreak the superconducting current in a superconducting material, inaccordance with embodiments of the present invention.

FIGS. 4A-4C illustrate sub-flux quantum generators in accordance withvarious embodiments of the present invention.

FIG. 5 illustrates a sub-flux quantum generator in which each turn in anN-turn ring encloses a different amount of area, in accordance with oneembodiment of the present invention.

FIG. 6 illustrates an array of persistent current qubits that are eachbiased by a sub-flux quantum generator, in accordance with oneembodiment of the present invention.

FIG. 7 illustrates a persistent current qubit in accordance with theprior art.

FIG. 8 illustrates a mesoscopic ring in accordance with the prior art.

Like reference numerals refer to corresponding parts throughout theseveral views of the drawings.

DETAILED DESCRIPTION

One embodiment of the present invention provides an N-turn ring that isused to trap fluxon or sub-fluxon amounts of magnetic flux whensuperconducting current flows through the N-turn ring. As observedexperimentally by Henry and Deaver in 1968, the magnetic flux trapped bya superconducting N-turn ring is quantized in multiples of h/N2e, whereN is the number of times an inaccessible region is encircled by theN-turn ring, h is Plank's constant, and e is elementary charge. SeeHenry and Deaver, 1968, Bull. Am. Phys. Soc. 13, 1691; and Olariu andPopescu, 1985, Rev. Mod. Phys. 57:2, pp. 339-436, especially pages412-413, which are hereby incorporated by reference in their entireties.This relationship assumes that each turn in the N-turn ring encirclesapproximately the same area. A two-turn superconducting ring can trapone half of a flux quantum (i.e. one half of a fluxon, 0.5×h/2e). AnN-turn ring has N turns. These N turns are optionally intertwined.Furthermore, in one embodiment of the inventive device, each turn of theN-turn ring includes a switch. By regulating the switches in the N-turnring, the amount of magnetic flux trapped in the N-turn ring can becontrolled with sub-fluxon precision.

One aspect of the present invention provides a sub-flux quantumgenerator that includes an N-turn ring made from superconductingmaterials. The sub-flux quantum generator can produce a stable andswitchable flux source with sub-fluxon precision. Sub-flux quantumgenerators have numerous applications in devices that require a reliablemagnetic field having a magnitude in the single fluxon or sub-fluxonrange. For example, the sub-flux quantum generators in accordance withthis aspect of the present invention can be used to reliably frustrate apersistent current qubit in order to make the basis states of thepersistent current qubit degenerate. In one case, the sub-flux quantumgenerators are used to frustrate circuit 700 with a magnetic flux havinga magnitude of one half of a fluxon, in order to make the two stablestates associated with the circuit degenerate.

FIG. 1 presents a generic embodiment of one embodiment of the invention.FIG. 1 illustrates a sub-flux quantum generator 100 that is capable oftrapping sub-fluxon magnitudes of magnetic flux. Sub-flux quantumgenerator 100 includes three components, (labeled 1, 2, and 3). They arean N-turn ring 1 of superconducting material, a switching device 2 tobreak the superconductivity of N-turn ring 1, and a magnetism device 3for presenting magnetic flux to N-turn ring 1. In some embodiments, eachturn (ring) in an N-turn ring of the present invention is made from adifferent material. Thus, for example, in some embodiments, a first turnin the N-turn ring is made from a first superconducting material and asecond turn in the N-turn ring is made from a second superconductingmaterial. As used herein, N is any integer greater than or equal to two.Thus, N=2, 3, 4, 5, 6,and so forth. Switching device 2 is used tointerrupt the superconducting current in N-turn ring 1 in a controllablefashion. Magnetism device 3 provides a magnetic flux that has asubstantial component normal with respect to the principle plane ofN-turn ring 1. Magnetism device 3 is used to generate magnetic flux thatis ultimately trapped by N-turn ring 1.

Description and Fabrication of N-Turn Ring 1

FIGS. 2A-2D illustrate a method of making an N-turn ring 1 in accordancewith one embodiment of the present invention. The exemplary fabricationprocess begins in FIG. 2A. A substrate 30 is presented with one sideprepared for material deposition and patterning. The actual choice ofmaterial for substrate 30 is application dependent. In some embodiments,substrate 30 is made of silicon, fused-silica (SiO₂), magnesium oxide(MgO), lanthanum aluminum oxide (LaAlO₃), quartz, or sapphire. In someembodiments, substrate 30 is made from alkali-free borosilicate glass(Shott AF45). Superconducting material is deposited on substrate 30 andpatterned to produce a turn 50 with an aperture 49 and a break 62between leads 61-1 and 61-2. Choices for substrate 30, and methods formaterial deposition and patterning of turn 50 are described in Van Zant,Microchip Fabrication, Fourth Edition, McGraw-Hill, New York, 1997;Rai-Choudhury, Microlithography, Micromachining and MicrofabricationVolume 1: Microlithography, The International Society for OpticalEngineering, Bellingham, Wash., 1997; and Madou, Fundamentals ofMicrofabrication, Second Edition, CRC Press, 2002, which are herebyincorporated by reference in their entireties. Leads 61 are used in across-over 60 that creates an N-turn ring in subsequent processingsteps.

In one embodiment, break 62 between leads 61-1 and 61-2 exceeds thecoherence length of the material used to form turn 50 in order to avoidstray Josephson effects. Coherence length is a material dependentphenomenon that arises because of the inability for superconductingelectron density to change instantaneously. A minimum length (coherencelength) is required to effectuate a change in the superconducting stateof an electrical current. For example, a transition from thesuperconducting state to a normal state will have a transition layer offinite thickness that is dependent upon the coherence length of thematerial in which this transition takes place. Experimental studies ofvarious superconductors has led to the following approximate values forcoherence length: Sn (230 nm), Al (1600 nm), Pb (83 nm), Cd (760 nm) andNb (38 nm).

In some embodiments, separation between leads 61-1 and 61-2 in excess ofthe coherence length of the material used to make turn 50 is desired inorder to avoid stray capacitance in break 62. Optionally, leads 55 arepatterned into ring 1. In one embodiment, leads 55 are placed atopposite sides of turn 50 as illustrated in FIG. 2A. In an embodiment ofthe present invention, turn 50 is made of a type I superconductor.Examples of type I superconductors include, but are not limited to,niobium (Nb), aluminum (Al), and lead (Pb).

In some embodiments, the material used to form turn 50, as with allmaterial layers described in conjunction with FIG. 2, is deposited ontosubstrate 30 using a process such as dc-magnetron sputtering or pulsedlaser deposition. The exact deposition process used will depend upon thenature of the compound used to make turn 50. Various deposition methodsknown in the art can be used depending on the properties material usedto form turn 50. Such known deposition methods include, but are notlimited to, chemical vapor deposition, low pressure chemical vapordeposition, reduced pressure chemical vapor deposition, atmosphericchemical vapor deposition, plasma assisted chemical vapor deposition,remote plasma chemical vapor deposition, anodic conversion, plasma spraydeposition, jet printing, sol-gel processes, vacuum evaporation, sputterdeposition (e.g., physical vapor deposition), collimated sputtering,laser ablated deposition, molecular beam deposition, ionized physicalvapor deposition, ion beam deposition, atomic layer deposition, hotfilament chemical vapor deposition, screen printing, electroless metaldeposition, or electroplating. See, for example, Van Zant, MicrochipFabrication, Fourth Edition, McGraw-Hill, New York, 1997; Rai-Choudhury,Microlithography, Micromachining and Microfabrication Volume 1:Microlithography, The International Society for Optical Engineering,Bellingham, Wash., 1997; and Madou, Fundamentals of Microfabrication,Second Edition, CRC Press, 2002. In addition to these depositiontechniques, those of skill in the art will recognize that there arenumber of other different methods by which layer 8010 may be depositedand all such methods are included within the scope of the presentinvention.

Once deposited, the superconducting material can be etched to form ring50 using, for example, carbon tetra-fluoride reactive ion etching(CF₄-RIE), argon (Ar) ion etching, or any other suitable deposition andetching techniques. In some embodiments, this patterning is assisted bydepositing a resist layer over the superconducting material, patterningthe resist layer using a photomask, etching the resist layer and theunderlying superconducting material, and then developing away the resistlayer in accordance with known lithographic methods.

Resists used to form a resist layer are typically comprised of organicpolymers applied from a solution. Generally, to coat the superconductingmaterial with resist, a small volume of the liquid is first dispensed onthe layer of superconducting material that overlays the substrate. Thesubstrate is then spun at a high rate of speed, flinging off excessresist and leaving behind, as the solvent evaporates, a resist layer. Insome embodiments, resist layer has a thickness in the range of 0.1 μm to2.0 μm.

In some embodiments, the resist layer that is applied over thesuperconducting material is an optical resist that is designed to reactwith ultraviolet or laser sources. In some embodiments, the resist layeris a negative resist in which polymers in the resist form a cross-linkedmaterial that is etch resistant upon exposure to light. Examples ofnegative resists that can be used to make the resist layer include, butare not limited to, azide/isoprene negative resists,polymethylmethacrylate (PMMA), polymethylisopropyl ketone (PMIPK),polybutene-1-sulfone (PBS), poly-(trifluoroethyl chloroacrylate) TFECA,poly-(2-methyl pentene-1-sulfone) (PMPS). In other embodiments, theresist layer is a positive resist. The positive resist is relativelyunsoluble. After exposure to the proper light energy, the resistconverts to a more soluble state. One positive photoresist in accordancewith the present invention is the phenol-formaldehyde polymer, alsocalled phenolformaldehyde novolak resin. See, for example, DeForest,Photoresist: Materials and Processes, McGraw-Hill, New York, 1975, whichis hereby incorporated by reference in its entirety. In someembodiments, the resist layer is LOR 0.5A, LOR 0.7A, LOR 1A, LOR 3A, orLOR 5A (MICROCHEM, Newton, Mass.). LOR lift-off resists usepolydimethylglutarimide.

After the resist layer has been applied, the density is ofteninsufficient to support later processing. Accordingly, in someembodiments of the present invention, a bake is used to densify theresist layer and drive off residual solvent. This bake is referred to asa softbake, prebake, or post-apply bake. Several methods of baking theresist layer are contemplated by the present invention including, butnot limited to, convection ovens, infrared ovens, microwave ovens, orhot plates. See, for example, Levinson, Principles of Lithography, SPIEPress, Bellingham, Wash., 2001, pp. 68-70, which is hereby incorporatedby reference in its entirety.

After the resist layer has been overlayed onto the superconductinglayer, the next step is alignment and exposure of the resist layer.Alignment and exposure is a two-purpose photomasking step. The firstpart of the alignment and exposure step is the positioning or alignmentof the required image on the wafer surface. The image is found on aphtotomask. The second part is the encoding of the image in the resistlayer from an exposing light or radiation source. In the presentinvention, any conventional alignment system can be used to align thephotomask with the resist layer, including but not limited to, contactaligners, proximity aligners, scanning projection aligners, steppers,step and scan aligners, x-ray aligners, and electron beam aligners. Fora review of aligners that can be used in the present invention, seeSolid State Technology, April 1993, p. 26; and Van Zant, MicrochipFabrication, Fourth Edition, McGraw-Hill, New York, 2000, pp. 232-241.

In one embodiment of the present invention, the tool used to project thepattern on the phtotomask onto the resist layer is a wafer stepper,e.g., a step-and-repeat stepper or a step-and-scan, stepper. See forexample, Levison, Principles of Lithography, SPIE Press, Bellingham,Wash., 2001, pp. 133-174, which is hereby incorporated by reference.After exposure through the phototmask the pattern for turn 50 is codedas a latent image in the resist layer as regions of exposed andunexposed resist. The pattern is developed in the resist by chemicaldissolution of the unpolymerized resist regions. There are severalmethods in which a developer can be applied to the resist in order todevelop the latent image. Such methods include, but are not limited to,immersion, spray development, and puddle development. In someembodiments of the present invention, wet development methods are notused. Rather, a dry (or plasma) development is used. In such dryprocesses, a plasma etcher uses energized ions to chemically dissolveaway either exposed or unexposed portions of the resist layer.

After development, an etching step is used to pattern thesuperconducting layer thereby forming turn 50. Exemplary etchingmethods, such as carbon tetrafluoride reactive ion etching (CF₄-RIE) andargon (Ar) ion etching have been referenced above. Additional etchingtechniques include, but are not limited to, wet etching, wet sprayetching, vapor etching, plasma etching, ion beam etching and reactiveion etching. See, for example, Stolz et al., Supercond. Sci. Technol. 12p. 806 (1999); Van Zant, Microchip Fabrication, Fourth Edition,McGraw-Hill, New York, 1997; Rai-Choudhury, Microlithography,Micromachining and Microfabrication Volume 1: Microlithography, TheInternational Society for Optical Engineering, Bellingham, Wash., 1997;and Madou, Fundamentals of Microfabrication, Second Edition, CRC Press,2002 which are hereby incorporated by reference in their entireties.

In general, structures can be patterned using the optical and/orelectron beam lithographic steps described above. As described below,the formation of the N-turn ring of the present invention typicallyrequires multiple layers with each layer requiring independentpatterning. In such instances, the lithographic steps described abovecan be repeated for each layer as necessary in order to accomplish suchpatterning.

In one embodiment of the present invention turn 50, with the exceptionof junction 61, has a uniform width T₅₀ that is greater than the Londonpenetration depth λ_(L) of the superconducting material used to maketurn 50. As used herein, at any given position in turn 50, width T₅₀ isthe shortest distance between interior 204 of turn 50 to exterior 202 ofturn 50 as illustrated in FIG. 2A. Such widths are desired so that turn50 will trap magnetic flux in aperture 49 when the turn issuperconducting. In some embodiments, the thickness of turn 50, withrespect to the plane of substrate 30 (normal to width T₅₀), is uniformand is on the scale (e.g., between 1× and 5×) of the London penetrationdepth λ_(L) of the superconducting material 50. This prevents theformation of weak spots where quantized magnetic flux may becometrapped. London penetration depths λ_(L) for some superconductingmaterials are: Sn (34 nm), Al (16 nm), Pb (37 nm), Cd (110 nm), and Nb(39 nm).

An intermediate material layer is deposited onto substrate 30 and turn50. This intermediate material is patterned to form shape 40 (FIG. 2B),thereby exposing elements of turn 50, such as element 60 (includingleads 61-1 and 61-2) and leads 55-1 and 55-2. In one embodiment of thepresent invention, the intermediate material layer is made from aninsulator such as aluminum-oxide (AlO_(x)) or silicon-oxide (SiO_(x)).In one example, superconducting material 50 is made from Nb and theintermediate material is 400 nm thick SiO_(x). In some embodiments,shape 40 has a width T₂₄₀ (FIG. 2B) that is less than T₅₀ (FIG. 2A).Embodiments where shape 40 has a width that is less than T₅₀ can requirethat shape 40 be made of an insulator with a low dielectric constant andhigh breakdown voltage. This is preferred in some embodiments in orderto prevent electrical coupling such as stray capacitance or currentshortage between individual turns within the N-turn ring.

In FIG. 2C, an additional turn is added to the structure illustrated inFIG. 2B. A superconducting material layer is deposited and patterned toform turn 51 using techniques similar to those used to pattern turn 50.In typical embodiments, the same superconducting material is used toform turns 50 and 51. Furthermore, in typical embodiments, turns 50 and51 have the same dimensions (e.g., same width T₅₀ as well as the samethickness). In some embodiments, turn 51 covers turn 50 withoutsubstantially obstructing aperture 49, regardless of whether turns 50and 51 have the same dimensions. As used herein, aperture 49 is alsotermed a common aperture.

FIG. 2D depicts crossover 60 in a perspective view. Lead 61-1 (notshown) and lead 61-2 of turn 50 are joined with leads 261-1 and 262-2 ofturn 51 to create a 30 double turn. In one embodiment of crossover 60,lead 61-1 (not shown) is coupled to lead 261-1 without coupling leads61-2 and 261-2. Some embodiments of the present invention includeadditional turns similar or identical to turn 50 and 51 and additionalinstances of crossover 60 that includes leads, thereby creating N-turnring 1. Each of the additional turns and leads has a width T₅₀ and athickness that exceeds the London penetration depth λ_(L) of thesuperconducting material used to make the turns. The N-turn ringstructure, such as two-turn ring 200 (FIG. 2D), can be used as a staticmagnetic flux source.

Because of the superconducting properties of N-turn ring 1, the magneticflux enclosed by N-turn ring 1 is quantized in multiples of h/N2e, whereN is the number of times an inaccessible region is encircled by theN-turn ring, h is Plank's constant, and e is elementary charge. Thus,the magnetic flux stored in N-turn ring 1 is Φ=n/N Φ₀, where n is equalto or greater than one, and N is the number of turns (e.g., number ofcrossovers 60) in the structure.

In some embodiments, the width T₅₀ (FIG. 2A) of each turn in the N-turnring is greater than the London penetration depth λ_(L) of the materialused to make the individual turns in the N-turn ring. In suchembodiments, the magnetic flux stored in the aperture 49 (FIG. 2C) ofthe N-turn ring can be trapped because it cannot penetrate through theN-turn ring when the N-turn ring is in a superconducting state. Escapeof the magnetic flux is possible when the superconductivity is broken ina global fashion. One method for breaking the superconductivity ofN-turn ring 1 such that it will no longer trap magnetic flux is to raisethe temperature of the ring above the critical temperature T_(C) of thematerial used to make the individual turns in the N-turn ring. However,in some applications, raising the temperature of the N-turn ring 1 isnot practical. For example, such an approach is unpractical when theN-turn ring 1 is used in a device in which other components must remainbelow the T_(C) of the material used to make N-turn ring 1. Furthermore,such an approach is unpractical in applications where the length of timethat it takes to release the magnetic flux trapped by the N-turn ring 1is critical (e.g., must be done quicker than the thermal transitionrates of the system allow).

The approach of adjusting the temperature of N-turn ring 1 finds usefulapplication when it is desirable to adjust the amount of flux that istrapped in N-turn ring. For example, in one embodiment of the presentinvention, the N-turn ring comprises at least one turn made of a firstsuperconducting material having a critical temperature T_(c1) and a atleast one turn made of a second superconducting material having acritical temperature T_(c2) where T_(c2) is different than T_(c1). Insuch embodiments, it is possible to adjust the amount of magnetic fluxtrapped by the N-turn ring by adjusting the temperature of the N-turnring. For example, consider the case in which the N-turn ring comprisesexactly one turn having a critical temperature T_(c1) and exactly turnhaving a critical temperature of T_(c2). A magnetic flux is applied tothe N-turn ring and then the N-turn ring is cooled to a temperatureT_(A), where T_(c1)<T_(A)<T_(c2). Thus, upon cooling to temperatureT_(A), the N-turn ring traps one flux quantum (h/N2e, where N is equalto one) because only one of the turns is superconducting. Then, at alater time, when it desired to reduce the magnetic flux trapped by theN-turn ring, the system is cooled to T_(B), where T_(B) is less thanT_(c1) and T_(c2). At such a point, both turns become superconductingand the N-turn ring traps only one half of a fluxon (0.5×h/2e).

Due to the disadvantages of relying on raising the temperature of N-turnring above the T_(c) for the ring, one aspect of the present inventionprovides an alternative method for releasing magnetic flux trapped inaperture 49 (FIG. 2A). This aspect of the invention uses switchingdevice 2 to break the superconductivity of each turn in N-turn ring 1.In one embodiment, switching device 2 is capable of introducing areversible topological cut into each turn in N-turn ring 1. There aremany devices that are capable of serving as switching device 2, and allsuch devices are within the scope of the present invention. Suchswitching devices include, but are not limited to, a cryotron, aJosephson junction, and a laser. These devices are switchable (e.g., canintroduce a reversible localized cut in the superconductivity of a turnin an N-turn ring) and can be used to permit flux in aperture 49 toescape or flux outside of two-turn ring 200 to enter.

Referring to FIG. 2D, the overall dimensions of an N-turn ring 1, suchas two-turn ring 200, are dependent upon the physical properties of thematerial used to make the turns in the N-turn ring. In one embodiment,the total area occupied by a turn (e.g., turn 50 or turn 51) in N-turnring 1 is less than the square of the coherence length of the materialused to make each turn. Coherence length is the smallest dimension overwhich superconductivity can be established or destroyed in a givensuperconductor. The coherence length of turns in N-turn ring 1 depend onthe type of material used to make each turn in the N-turn ring as wellas the purity of such material. For example, the addition of impuritiesto a metal can cause the coherence length of the metal to decrease. Thecoherence length of some superconducting materials are as follows tin(30 nm), aluminum (1600 nm), lead (83 nm), cadmium (760 nm), and niobium(38 nm). Thus, in the case where a turn in N-turn ring 1 is made of pureniobium, the turn can occupy an area that is no larger than 1444 nm², inaccordance with one embodiment of the present invention. In someembodiments of the present invention, the total area occupied by a turn(e.g., turn 50 or turn 51) in N-turn ring 1 is less than the square ofthe coherence length of the superconducting material used to make eachturn and the width T₅₀ (FIG. 2A) of each turn is less than the Londonpenetration depth λ_(L) of the superconducting material.

In some embodiments of the present invention, N-turn ring 1 is amesoscopic system. A mesoscopic system is one that is described byquantum mechanical principles rather than classical mechanicalprinciples. Mesoscopic systems are non-microscopic because they consistof many atoms. The term mesoscopic is a well used term in the field ofphysics and, in general, indicates a device of physical dimension suchthat phenomena observed on the structure require quantum mechanicalexplanation. In other words, mesoscopic systems refer to a class ofsolid systems where the quantum mechanical single particle accuratelydescribes the characteristics of the physical system. In someembodiments, mesoscopic systems are the systems of intermediate size,e.g., macroscopic but small enough (less than or equal to 10⁻⁴ cm). Inmesoscopic systems, quantum interference is very important, since at lowenough temperatures (<1 K) the phase coherence length of quasiparticles(“electrons”) exceeds the size of the system. See, for example,Zagoskin, Quantum Theory of Many-Body Systems, pp. 19-20, Springer,1998; and Imry, “Physics of Mesoscopic Systems”, in Directions inCondensed Matter Physics: Memorial Volume in Honor of Shang-Keng Ma,Grinstein and Mazenko, eds., World Scientific, 1986, which are herebyincorporated by reference in their entireties.

In some embodiments, an N-turn ring 1 is mesoscopic when the respectiveoverall dimensions (overall height, overall length, and overall width)of the N-turn ring are each less than the phase coherence length of thematerials used to make the N-turn ring. In some embodiments, an N-turnring 1 is mesoscopic when it has respective overall dimensions (height,length, width) of about 10⁻⁶ meters or less, is cooled to a temperaturebelow the critical temperature of the superconducting materials used tomake the N-turn ring, and has overall dimensions that are respectivelysmaller than the phase coherence length of charges in the N-turn ring.

Description and Fabrication of Selected Switching Devices 2

One switching device 2 that can be used to break the superconductivityof one or more rings in N-turn ring 1 is a cryotron. FIGS. 3A-3C detaila method used to fabricate an exemplary cryotron. The exemplary cryotronincludes outer layers and intermediate insulating layers. The outerlayers form coils that conduct current while the insulating intermediatelayers are positioned around the one or more rings in N-turn ring 1.When a current of sufficient size is run through the outer layers of thecryotron, the magnetic field inductively generated at the center of thecryotron interrupts the superconducting current in the one or more ringsof N-turn ring 1.

Referring to FIG. 3A, on a substrate 30, material is deposited andpatterned to form outer layer 301. In some embodiments, it is convenientto have outer layer 301 patterned as strips, as illustrated in FIG. 3A.However, there is no requirement that outer layer 301 be patterned asstrips. Preferably, the material used for outer layer 301 is able toconduct electrical current. Therefore, suitable materials for outerlayer 301 include semiconducting materials (e.g., silicon, germanium),conducting materials (e.g., copper, silver, and gold), orsuperconducting materials (e.g., type I superconductors, type IIsuperconductors, gallium, aluminum, indium, tin, lead, niobium, andniobium-tin).

Next, first insulating layer 310 is deposited on a central portion ofouter layer 301 (e.g., a central portion of the disjoint pieces thatcomprise layer 301). After the patterning of first insulator layer 310,the ends of outer layer 301 are exposed, as depicted in FIG. 3B. Next,intermediate layer 320 (FIG. 3B) is deposited on insulator layer 310. Insome embodiments, intermediate layer 320 is made from any material usedto make outer layer 301, including semiconducting materials (e.g.,silicon, germanium), conducting materials (e.g., copper, silver, andgold), or superconducting materials (e.g., type I superconductors, typeII superconductors, gallium, aluminum, indium, tin, lead, niobium, andniobium-tin). In some embodiments, layer 320 is patterned into one ormore turns of an N-turn ring 1. For example, in some embodiments,intermediate layer 320 comprises layer 50 and/or layer 51 (FIG. 2).Thus, in such embodiments, intermediate layer 320 is typically made frommaterials such as a type I superconductor (e.g., niobium, aluminum, andlead) or a type II superconductor.

In some embodiments, insulator layer 310 is thick enough to electricallyseparate outer layer 301 from intermediate layer 320. For instance, inone embodiment, where outer layer 301 and intermediate layer 320 aremade from superconducting materials, insulator layer 310 is deeper thanthe longest superconducting coherence length of the superconductingmaterials used to make layers 301 and 320. In some embodiments, outerlayer 301 and intermediate layer 320 each comprise a single layer ofmaterial. In other embodiments, outer layer 301 and intermediate layer320 each comprise several discrete layers of material.

In FIG. 3C, a second insulator layer 311 is deposited over intermediatelayer 320 and patterned using the lithographic techniques describedabove. The material used to make insulator layers 310 and 311 isdependent upon the physical properties of the material used to makeintermediate layer 320. In the case where intermediate layer 320 is madefrom niobium or aluminum, insulator layers 310 and 311 are typicallymade of aluminum oxide (Al₂O₃). In some embodiments, insulator layers310 and/or 311 are made from silicon oxide. Further, those of skill inthe art will appreciate that insulator layers 310 and 311 can be madefrom other materials and all such materials are within the scope of thepresent invention.

Once second insulator layer 311 has been deposited, outer layer 302 isdeposited over layer 311. Then outer layer 302 is patterned in such away as to create, in conjunction with outer layer 301, a multiplewinding solenoid around first insulator 310, intermediate layer 320, andsecond insulator layer 311. Accordingly, outer layer 302 is typicallymade out of the same materials as outer layer 301. In some embodiments,outer layer 302 has the shape of disjoint strips that connect with thedisjoint strips of outer layer 301 to form coils around the insulatingand intermediate layers, as illustrated in FIG. 3C. In otherembodiments, outer layer 302 has the shape of a single sheet. One ofskill in the art will appreciate that other shapes for outer layers 301and 302 are possible and all such shapes are within the scope of thepresent invention. Outer layers 301 and 302 together with insulatorlayers 310 and 311, as pictured in FIG. 3C, form cryotron 300. Cryotron300 represents one form of switching device 2 that can be used to breakthe superconductivity of N-turn ring 1.

Now that the methods used to manufacture cryotron 300 have beendisclosed in accordance with one embodiment of the present invention,the operation of cryotron 300 will be described. The operation ofcryotron 300 includes driving a current through layers 301 and 302 sothat a magnetic field is created in the interior of cryotron 300. In thecase where intermediate layer 320 is superconducting, the material usedto make outer layers 301 and 302 is selected such that layers 301 and302 conduct a current that exceeds the critical field of intermediatelayer 320. The maximum field that can be applied to a superconductor ata given temperature without loss of superconductivity is referred to asthe critical field of the superconductor. The critical field varies intype I and type II superconductors. The maximum critical field (H_(C))in any type I superconductor is about 2000 Gauss (0.2 Tesla), but intype II materials superconductivity can persist to several hundredthousand Gauss (H_(C2)). At fields greater than H_(C) in a Type Isuperconductor and greater than H_(c2) in a type II superconductor, thesuperconductor reverts to the normal state and regains its normal stateresistance.

Because the critical field of type II materials is so high, intermediatelayer 320 (e.g., turns 50 and 51 of FIG. 2) is typically made of a typeI superconductor. In the case where intermediate layer 320 is made fromAl (or a superconducting material with a similar H_(C)), layers 301 and302 must conduct enough current to produce a magnetic field that isbetween 50 Gauss and 500 Gauss. In another example, in the case whereintermediate layer 320 is made from Nb (or a superconducting materialwith a similar H_(C)), layers 301 and 302 must conduct enough current toproduce a field of about 2000 Gauss. One Tesla is equal to about 10⁴Gauss. The conductivity of layers 301 and 302 is determined by theirdimensions and the material used to form the layers. The magnetic fieldproduced by layers 301 and 302 is a function of the number of coils thatlayers 301 and 302 form around intermediate layer 320 and the amount ofcurrent in these coils. In one embodiment of the present invention,cryotron 300 is used to introduce local breaks in the superconductivityin select turns in the N-ring 1.

FIGS. 3D-3F describe the manufacture of another switching device 2 thatis used in some embodiments of the present invention. In particular,FIGS. 3D-3F describe how Josephson junctions are introduced into one ormore turns of N-turn ring 1 in some embodiments of the invention. InFIG. 3D, a superconducting material is deposited onto substrate 40 andpatterned into a single piece 331 that includes a biasing lead 332. Insome embodiments, piece 331 is a part of a turn in the N-turn ring 1.For example, in some embodiments, piece 331 is part of turns 50 or 51(FIG. 2).

In FIG. 3E, a material is layered onto a portion of piece 331 to formJosephson layer 340. Many different materials can be used to formJosephson layer 340. In one example, Josephson layer 340 is aninsulating layer with a depth that is less than or equal to thecoherence length of the superconducting material used to make piece 331.In such embodiments, Josephson layer 340 acts as a tunneling barrier.When Josephson layer 340 is an insulator, the layer is deposited suchthat it has a depth that is less than approximately the coherencelength, ξ, of the superconducting material used to make piece 331. Inanother embodiment, Josephson layer 340 is formed by using a cleannormal metal. In such embodiments, the depth of layer 340 is generallyless than the approximate correlation length of the clean normal metalused to form Josephson layer 340. The correlation length of a cleannormal metal is

ν_(F)/kT, where

is Planck's constant over 2π, ν_(F) is the Fermi velocity of the metal,and kT is the thermal energy. Still other Josephson layers 340 arepossible. For example, a dirty normal metal junction with scatteringsites could be used to from Josephson layer 340. See Barone and Paternò,Physics and Applications of the Josephson Effect, John Wiley & Sons, NewYork (1982), which is hereby incorporated by reference in its entirety.One of skill in the art will appreciate that still other materials canbe used to form Josephson layer 340, and all such materials are withinthe scope of the present invention.

In FIG. 3F, an additional superconducting piece 335 is deposited ontoJosephson layer 340 and patterned to include lead 336. In someembodiments, pieces 331 and 335 are portions of the same turns in N-turnring 1. Accordingly, in such embodiments, piece 331 is made of the samematerial as piece 335 (e.g., a type I superconductor). In embodimentswhere piece 331 and piece 335 are different sections of the same turn inN-ring 1, the net effect of the processing steps illustrated in FIGS.3D-3F is the introduction of a Josephson junction 350 into the ring.

Josephson junction 350 may be used to locally break thesuperconductivity of a turn in N-turn ring 1. Generally, a Josephsonjunction, such as Josephson junction 350, can operate in a zero voltagestate or a voltage state. The zero voltage state is a superconductingstate whereas the voltage-state is a non-superconducting state. Aproperty of all Josephson junctions is their ability to switch from azero voltage to a voltage state when the current through the Josephsonjunction is greater than a critical current I_(C). To produce such acritical current, leads 332 and 336 are used to introduce a currentthrough Josephson junction 350. When this current exceeds the I_(C) oflayer 340, Josephson junction 350 is toggled from a zero voltage state(superconducting) to a voltage state (nonsuperconducting). Therefore,Josephson junction introduces a local break in the superconductivity ofa turn in N-turn ring 1.

FIG. 3G depicts another switching device 2 (device 375) that can be usedto break the superconductivity of one or more turns in N-turn ring 1.Focused electromagnetic radiation, such as light from a laser, appliedto a superconductor will break the superconducting current withinsuperconductor. The laser raises the temperature of a localized portionof the N-turn ring 1 above the critical temperature of the ring, therebyinterrupting the supercurrent in a localized fashion. This phenomenon isused in system 380. System 380 includes a laser 360. In someembodiments, laser 360 is an infrared (IR) laser. In some embodiments,laser 360 has a wavelength in the range of 0.7 ΦM to about 10 ΦM. Insome embodiments, laser 360 is an Alexandrite laser with a wavelength ofabout 0.72 ΦM, a GaAlAs diode laser with a wavelength of about 0.72 ΦM,a Ti-Sapphire laser with a wavelength of about 0.88 ΦM, an InGaAs diodelaser with a wavelength of about 0.98 ΦM, a Nd-Yag laser with awavelength of about 1.06 ΦM, a He—Ne laser with a wavelength of about1.15 ΦM, an Nd-YLF laser with a wavelength of 1.31 ΦM, or a Nd-YAG laserwith a wavelength of about 1.32 ΦM.

In some embodiments, laser 360 has a wavelength in the visible spectrum(0.7 ΦM. to 0.4 ΦM) or ultraviolet spectrum (0.4 ΦM. to 0.15 ΦM).However, the heating effect associated with lasers operating in theultraviolet wavelength range is advantageous and has utility in someembodiments of the present invention. Therefore, lasers operating in theultraviolet wavelength range are more commonly used in systems 380 inaccordance with the present invention.

In some embodiments, laser 360 is a pulsed laser. In some embodiments,the pulse duration of laser 360 is 100 femtoseconds, 50 femtoseconds, 10femtoseconds, 5 femtoseconds, 1 femtosecond, or less. In someembodiments, laser 360 has a wavelength of about one micron 1 ΦM and apulse duration of about 10 femtoseconds or less. In some embodiments,laser 360 has a pulse duration that is about the length of the magneticdiffusion time of N-turn ring 1. The magnetic diffusion time for aconductor such as N-turn ring 1 is the amount of time needed toannihilate a field inside the conductor. The magnetic diffusion time isdependent on the conducting material and the dimensions (size) of thematerial. Pulse durations that approximate or exceed the magneticdiffusion time of N-turn ring 1 are desirable because they insure thatthe supercurrent is interrupted for a sufficiently long time to createor annihilate the flux trapped inside the ring.

Referring to FIG. 3G, laser 360 is directed down waveguide 370 andprojected onto a superconducting structure, such as two-turn ring 200(see FIG. 2D). The electromagnetic radiation travelling down waveguide370 can be modulated by an optional switch 365. Examples of switches 365are well known in the art. In some embodiments, waveguide 370 comprisesa plurality of waveguides and modulating switch 365 acts as adistributor of the electromagnetic radiation (not shown). This pluralityof waveguides can be directed on to different portions of two-turn ring200.

In system 380, waveguide 370 terminates at a distance d₃₇₀ away from aregion of two-turn ring 200. The distance d₃₇₀ can be a distance of zeroto several centimeters or more. Those of skill in the art willappreciate that, at larger distances, such as several centimeters, aprecision optical system between waveguide 370 and two-turn ring 200 canbe used to align the waveguide with specific regions of N-turn ring 1.

Sub-Flux Quantum Generator 400

FIG. 4A illustrates a device 400 that includes a two-turn ring 200(exemplary N-turn ring 1, FIG. 1), switching devices 405 to break thesuperconductivity of ring 200 (exemplary switching device 2, FIG. 1),and a magnetic flux source 412 (exemplary magnetism device 3, FIG. 1).In FIG. 4A, two-turn ring 200 is incorporated into device 400 throughleads 55. Examples of switches 405 include, but are not limited to, acryotron 300 (FIG. 3C), a Josephson junction 350 (FIG. 3F), and a laser375 (FIG. 3G). In the example illustrated in FIG. 4A, switch 405 isplaced in each turn of a two-turn ring.

An alternating current source 412 (magnetic flux source 3) and a directcurrent source 411 are arranged parallel and are in electricalcommunication with two-turn ring 200 in order to create a supercurrentthrough two-turn ring 200. In state 1, switches 405 allow current toflow and supercurrent travels equally through both turns of two-turnring 200. Similarly, when two-turn ring 200 is replaced with ageneralized N-turn ring, current flows through each turn of the N-turnring. Further, the current flows equally through both possible paths(paths 470 and 480) of the ring from 55-1 to 55-2. Thus, there is adirect connection 198 (path 480) and an indirect connection 199 (path470) through crossover 60. In the embodiment illustrated in FIG. 4A,two-turn ring 200 includes crossover 60. Because the current in paths470 and 480 are equal and flowing in opposite directions, no magneticfield is induced in aperture 49 during initial state 1.

In state 2, switches 405 are set to block the flow of current. As aresult, the superconducting current that was flowing in path 480 instate 1 is terminated. Supercurrent can only travel through connection198 of ring 200 (path 470) because connection 198 does not include thelocalized break induced by switches 405. As a result, the symmetrybetween the superconducting current following paths 470 and 480 is lostand, therefore, a net magnetic flux Φ_(X) is induced into aperture 49during state 2. In state 3, the symmetrical superconducting current isrestored to two-turn ring 200 by closing switches 405, allowing currentto flow through connection 199 (path 480). In a typical embodiment, eachturn in two-turn ring 200 has a width T₅₀ (FIG. 2A) that exceeds theLondon penetration depth λ_(L) of the material used to make device 200.Therefore, the magnetic flux that arose in aperture 49 during state 2 istrapped and quantized during state 3. In this example, the amount ofmagnetic flux that is trapped in aperture 49 (Φ_(X)) is n/2Φ₀, where theinteger n is controlled by the amount of supercurrent conducted through2-turn ring 200, and the value 2 is found in the equation for the Φ_(X)of two-turn ring 200 because there are two turns in device 200. Ingeneral, the induced magnetic flux is equal to the product of theelectrical current flowing in device 200 during state 2 and theself-inductance of device 200. When the current is not superconducting,the induced magnetic flux can take any value. However, when device 200becomes superconducting, the magnetic flux becomes quantized. For thisreason, the magnetic flux that is trapped in aperture 49 (Φ_(X)) isn/2Φ₀.

The rate at which flux can be introduced into aperture 49 is applicationdependent. In the embodiment illustrated in FIG. 4, the rate isapproximately equal to τ_(m) the magnetic diffusion timeτ_(m)≈μ_(o)·σ·L² where μ_(o) is the permeability of free space, σ is thenormal conductivity of superconducting material 50 and L is proportionalto the mean width of two-turn ring 200.

Sub-Flux Quantum Generator 401

FIG. 4B illustrates another sub-flux source in accordance with thepresent invention. Sub-flux quantum generator 401 includes a two-turnring 200 that is a variant of the two-turn ring 200 illustrated in FIG.4A. The two-turn ring illustrated in FIG. 4B includes two crossovers 60and three switches 405 (switching devices 2). Operation of sub-fluxquantum generator 401 is similar to that of sub-flux quantum generator400. It is possible to trap a flux Φ_(X) in two-turn ring 200. Thismagnetic flux can be established in aperture 49 even when an externalflux Φ_(E) (not shown) is present.

In state 1, for sub-flux quantum generator 401, switches 405 allowcurrent to flow and supercurrent travels equally through all turns ofthree-turn ring 200 which may be replaced by an N turn ring. Further,the current flows equally through both possible paths (472 and 482) ofring 200 from 55-1 to 55-2. There is a direct connection 198 (path 482)and an indirect connection 199 (path 472) through crossovers 60-1 and60-2. Because the current in paths 472 and 482 are equal and flowing inthe same principle direction, no magnetic field is induced in aperture49 during initial state 1.

In state 2, switches 405 no longer allow current to flow and thesuperconducting current that was flowing through path 470 in state 1 isblocked by switches 405-1, 405-2, and 405-3. Current must flow throughdirect connection 198 (path 482). As a result, the symmetry between thecurrent flowing in paths 472 and 482 that existed in state 1 is lostand, therefore, a magnetic flux Φ_(X) is induced into aperture 49 duringstate 2. In state 3, the symmetrical superconducting current is restoredto two-turn ring 200 by closing switches 405, allowing current to flowalong path 472 (through connection 199). In a typical embodiment, eachturn in an N-turn ring 200 has a width T₅₀ (FIG. 2A) that exceeds theLondon penetration depth λ_(L) of the material used to make device 200.Therefore, the magnetic flux that arose in aperture 49 during state 2 istrapped and quantized during state 3. In this example, the amount ofmagnetic flux that is trapped in aperture 49 (Φ_(X)) is n/3Φ₀, where theinteger n is controlled by the amount of supercurrent conducted through3-turn ring 200, and the value 3 is found in the equation for the Φ_(X)of three-turn ring 200 because there are three rings in device 200. Therate at which flux can be introduced into aperture 49 is applicationdependent. In the embodiment illustrated in FIG. 4, the rate isapproximately equal to τ_(m) the magnetic diffusion timeτ_(m)≈μ_(o)·σ·L² where μ_(o) is the permeability of free space, σ is thenormal conductivity of superconducting material 50 and L is proportionalthe mean width of two-turn ring 200.

Sub-Flux Quantum Generator 402

FIG. 4C illustrates another sub-flux quantum generator (402) inaccordance with an embodiment of the present invention. Sub-flux quantumgenerator 402 includes an N-turn ring 200 and a switch 406 that shuntscrossover 60-2 in N-turn ring 200. Operation of sub-flux quantumgenerator 402 differs from that of sub-flux quantum generators 400 (FIG.4A) and 401 (FIG. 4B). In particular, the number of turns in N-turn ring1 may be adjusted by operation of switch 406.

Magnetic flux in sub-flux quantum generator 402 is trapped byprogression through the following states. In state 1, switches 405 inthe rings of N-turn ring 200 in which magnetic flux is to be trapped areopened. A current is driven through N-turn ring 200, establishingmagnetic flux Φ_(X) in aperture 49. In state 2, the magnetic flux istrapped in aperture 49 by closing switches 405 in specific rings ofN-turn ring 1. The amount of magnetic flux trapped in state 2 is afunction of the number of switches 405 closed, the state of shuntingswitch 406, and the amount of current flowing through N-turn ring 1 whenswitches 405 were closed. For example if a flux Φ_(X)=n/2 Φ₀ is desired,switches 405-1, 405-2 and 406 are closed in state 2 while switch 405-3remains open. When switches 405 and 406 are in this configuration, themagnetic flux is enclosed in a two-turn superconducting ring. Therefore,the magnetic flux assumes the quantized value of Φ_(X)=n/2 Φ₀. In theexpression for Φ_(X), the value n is a function of current driventhrough N-turn ring 1, and the value 2 in denominator arises becausethere are two turns in the N-turn ring.

Sub-flux quantum generator 402 can be used to trap magnetic flux Φ_(X)having the quantized value n/3 Φ₀ by progression through the followingstates. First, switches 405-1, 405-2, and 405-3 are opened. A current isdriven through N-turn ring 200, establishing magnetic flux Φ_(X) inaperture 49. Then switch 406 is opened and switches 405-1, 405-2, and405-3 are closed. Leaving switch 406 open activates crossover 60-2 andopens up a third superconducting ring around aperture 49. As a result,the amount of magnetic flux that is trapped by aperture 49 is n/3 Φ₀.

One of skill in the art will appreciate that the sub-flux quantumgenerator 402 could be modified to have N rings and at least N−1crossovers, where N is any integer greater than 2. Further, shuntswitches could be placed across any number of the at least N−1crossovers. In this way, a sub-flux quantum generator that is capable oftrapping a magnetic flux Φ_(X)=n/N Φ₀ is realized, where N is determinedby the configuration of the switches 405 and shunt switches 406 (notshown) in the N-turn ring 1. Such devices can be used as calibrationunits for magnetometers. Since the value of the flux Φ_(X) can beaccurately determined, the device can be used to check the accuracy andprecision of any device that senses magnetic flux. Devices that sensemagnetic flux include a superconducting quantum interference device(SQUID) and a magnetic force microscope (MFM).

Sub-Flux Quantum Generator 500

FIG. 5 illustrates a sub-flux quantum generator 500 in accordance withanother embodiment of the present invention. Previously, it has beendisclosed that the amount of magnetic flux trapped by an N-turnsuperconducting ring is quantized into some multiple of h/N2e where N isthe number of turns in the N-turn ring. This relationship assumes thatthe area within each turn in the N-turn ring is approximately the same.In sub-flux quantum generator 500, at least one turn in the N-turn ring1 encloses an area A₁ that is larger or smaller than the area A₂enclosed by another turn in the N-turn ring. Thus, although the N-turnring 1 in sub-flux quantum generator still traps a quantized amount ofmagnetic flux when in the superconducting state, the amount of magneticflux trapped by the N-turn ring 1 is not governed by the expressionh/N2e. In fact, the amount of magnetic flux stored by N-turn ring 1 canbe adjusted by varying the size of individual rings in the N-turn ring1. In the embodiment illustrated in FIG. 5, for example, N-turn ring 1has two turns. The outer turn encloses area A₁ and the inner turnencloses area A₂. Here, the two-turn ring traps magnetic flux atquantized values that diverge from n/2 Φ₀, where n is a natural number,because each turn encloses a different area. Thus, the amount ofmagnetic flux that the N-turn ring traps in sub-flux quantum generator500 can be modified by adjusting the size of each turn of the N-turnring.

In some embodiments, it is desirable to introduce an inhomogeneousmagnetic field into N-turn ring 1. An inhomogeneous magnetic field isone that varies in magnitude as a function of position within aperture49 (e.g., the magnetic field has a gradient in at least one directionwithin aperture 49).

Thus, an inhomogeneous magnetic field in the case of the N-turn ring 1arises when the magnitude of the trapped magnetic flux within aperture49 (FIG. 5) of the N-turn ring varies as a function of position. FIG. 5illustrates how an inhomogeneous magnetic field within aperture 49 canbe achieved. FIG. 5 includes a magnetic flux source 550 that includes acurrent source 551 and an inductor 553. In FIG. 5, current source 551 isused to drive a current through N-turn ring 1. Devices (not shown inFIG. 5) such as cryotrons 300 (FIG. 3C), Josephson junctions 350 (FIG.3F), and/or laser systems 380 are used to break the superconductingcurrent at localized positions of the turns in N-turn ring 1. At a laterstage these localized breaks are restored in order to trap magnetic fluxin the aperture of the N-turn ring using the techniques described abovefor other embodiments of the present invention. In FIG. 5, a magneticfield within aperture 49 that is inhomogeneous is produced usingadditional flux generator 501. Current in 501, from alternating currentsource 560 and direct current source 562, produces a magnetic flux inaperture 49. The magnitude of this flux at any given point in aperture49 is inversely dependent on the distance between the point in aperture49 and the current in 501. Other geometrical configurations of 501 arepossible. Additional flux generator 501 includes an alternating currentsource 560 that is configured to provide a magnetic field at a differentangle than the flux that is enclosed within the N-turn ring. This isaccomplished by providing a wire adjacent to the ring 1 out of the planeof the ring. Using current sources 560 and 562 a current in 501 willprovide a flux that is not normal to the plane of 1. Further, fluxgenerator 500 can include a charge source 562 that makes the magneticfield in the N-turn ring inhomogeneous. FIG. 5 illustrates anotherdevice that can be used to make the magnetic field in an N-turn ringinhomogeneous. The device is capacitor 510, which is capable of bendingthe magnetic field within the ring.

Use of Sub-Flux Quantum Generators to Bias Persistent Current Qubits

FIG. 6 illustrates an embodiment of the present invention in which asub-flux quantum generator is used to frustrate a superconductingstructure. An example of a superconducting structure is asuperconducting qubit, such as a persistent current qubit 700. Asdescribed above, persistent current qubit 700 (FIG. 6, FIG. 7) comprisesa superconducting loop that has at least three Josephson junctions 702.The Josephson energy of two of the junctions 702 is equal while theJosephson energy of the third junction 702 is slightly less than theother two junctions. In FIG. 6, the presence of a Josephson junction 702is indicated by an “X”. The size of the “X” used to label each Josephsonjunction 702 is proportional to the Josephson energy of the respectivejunction.

In FIG. 6, each sub-flux quantum generator in 400 is used to bias apersistent current qubit 700 so that the two stable energy states of thequbit become degenerate (i.e., have equal energy). These degeneratestates correspond to quantum phase states of persistent current qubit700. Using these states, which may be ground states of persistentcurrent qubit 700, it is possible to perform quantum computationoperations. Those of skill in the art will appreciate that, in someembodiments, it is necessary to shield the persistent current qubit fromleads 55 (FIG. 4A).

In additional embodiments of the present invention, a sub-flux quantumgenerator is used to bias any superconducting qubit, such as phasequbits and/or charge qubits and/or hybrid qubits. Qubits are defined bytheir uncertainty in charge and phase, which is, in turn, determined bythe Heisenberg uncertainty principle. The Heisenberg uncertaintyprinciple can be expressed as ΔnΔφ≦½, where Δn represents an uncertaintyin the charge of the qubit and Δφ represents an uncertainty in the phaseof the qubit. There are two classic types of qubits, charge qubits andphase qubits. In a charge qubit, the uncertainty of the phase of thequbit is large compared to the uncertainty of the charge. In a phasequbit, uncertainty of the charge of the qubit is large compared to theuncertainty of the phase. When a qubit is in the charge regime, thecharge of the charge device represents a good quantum number and has afinite number of charge states. A good quantum number in this case meansa small uncertainty in its charge. See, e.g., Nakamura et al., 1999,Nature 398, p. 786, which is hereby incorporated by reference. When aqubit is in the phase regime, the phase of a mesoscopic phase device isa good quantum number (to the extent that the uncertainty is small)having a finite number of phase states. A hybrid qubit is a qubit thathas neither a charge nor a phase as a good quantum number. An example ofa hybrid qubit is a quantronium. See, for example, Cottet et al., 2002,Physica C 367, pp. 197-203; and Vion et al., 2002, Science 296, pp. 886,which are hereby incorporated by reference in their entireties.

Further, one or more sub-flux quantum generators can be used tofrustrate (bias) a superconducting structure, such as a qubit. In someembodiments, the frustration is used to create degenerate states as inthe case illustrated in FIG. 6. In other embodiments, this frustrationneed not create degenerate states. Rather, the frustration can be usedto bias two stable states of the superconducting structure so that theyhave a predetermined energy differential. A case where the use ofnon-degenerate stable states is useful is described in Lidar et al.,2002, “Quantum Codes for Simplifying Design and Suppressing Decoherencein Superconducting Phase-Qubits,” Quantum Information Processing 1, p.155, also published as LANL preprint ArXiv.org:cond-mat/0204153 (2002),which is hereby incorporated by reference in its entirety.

The embodiment of the present invention depicted in FIG. 6 shows anarray of coupled qubits. These qubits (e.g., qubits 601-1 and 601-2) arepersistent current qubits and are coupled through an LC-circuit orresonance circuit 610. Here the LC-circuit includes an inductor 608 anda capacitor 609. This pairwise coupling can be repeated in order tocouple many pairs of qubits to other pairs of qubits. Such a groupingcan serve as a component of a larger quantum-computing device, such as aquantum register or quantum computer.

The operation of persistent current qubit 700 in some quantum computingoperations involves applying quantum gates to the qubit. A quantum gateis a controlled interaction between qubits that produces a coherentchange in the state of one qubit that is contingent upon the state ofanother qubit. See, for example DiVincenzo in Braunstein and Lo (eds.),Scalable Quantum Computers, Wiley-VCH Verlag GmbH, Berlin (2001);Makhlin et al., 2001, Reviews of Modern Physics 73, p. 357; and Nielsenand Chuang, Quantum Computation and Quantum Information, CambridgeUniversity Press, 2000, which are hereby incorporated by reference intheir entireties. These gates include a biasing operation that makes onebasis state energetically favorable over the other. A method toaccomplish such a biasing operation is to provide a flux bias byapplication of an external magnetic field. Such biasing operations aredetailed in Orlando et al., 1999, Phys. Rev. B 60, 15398, which ishereby incorporated by reference in its entirety.

ALTERNATIVE EMBODIMENTS

All references cited herein are incorporated herein by reference intheir entirety and for all purposes to the same extent as if eachindividual publication or patent or patent application was specificallyand individually indicated to be incorporated by reference in itsentirety for all purposes. While the present invention has beendescribed with reference to a few specific embodiments, the descriptionis illustrative of the invention and is not to be construed as limitingthe invention. In particular, while various embodiments of the presentinvention have been described with a two-turn ring, those of skill inthe art will appreciate that an N-turn ring, where N is any integerequal to or greater than two, can be used in such embodiments. Variousmodifications may occur to those skilled in the art without departingfrom the true spirit and scope of the invention as defined by theappended claims.

1. A sub-flux quantum generator comprising: an N-turn ring comprising aplurality of connected turns about a common aperture, wherein a widthT₅₀ of each respective turn in said plurality of connected turns exceedsthe London penetration depth of a superconducting material used to makethe respective turn; a switching device configured to introduce alocalized reversible break in a superconducting current in at least oneturn in said plurality of connected turns; and a magnetism deviceconfigured to generate a magnetic field within said common aperture.2-42. (canceled)